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A063841
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Table T(n,k) giving number of k-multigraphs on n nodes (n >= 1, k >= 0) read by antidiagonals.
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7
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1, 1, 1, 1, 2, 1, 1, 3, 4, 1, 1, 4, 10, 11, 1, 1, 5, 20, 66, 34, 1, 1, 6, 35, 276, 792, 156, 1, 1, 7, 56, 900, 10688, 25506, 1044, 1, 1, 8, 84, 2451, 90005, 1601952, 2302938, 12346, 1, 1, 9, 120, 5831, 533358, 43571400, 892341888, 591901884, 274668, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| The first five rows admit the g.f. 1/(1-x), 1/(1-x)^2, 1/(1-x)^4 and those given in A063842, A063843. Is it known that the n-th row admits a rational g.f. with denominator (1-x)^A000124(n)? - M. F. Hasler, Jan 19 2012
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LINKS
| Harald Fripertinger, The cycle type of the induced action on 2-subsets
Vladeta Jovovic, Formulae for the number T(n,k) of n-multigraphs on k nodes
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EXAMPLE
| Table begins
1 1 1 1 ...
1 2 3 4 ...
1 4 10 20 ...
1 11 66 276 ...
T(3,2)=10 because there are 10 unlabelled graphs with 3 nodes with at most 2 edges connecting any pair.
(. . .),(.-. .),(.-.-.),(.-.-.-),(.=. .),(.=.=.),(.=.=.=),(.-.=.),(.-.-.=),(.=.=.-) -Geoffrey Critzer, Jan 23 2012.
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MATHEMATICA
| (* This code gives the array T(n, k). *) Needs["Combinatorica`"]; Transpose[Table[Table[PairGroupIndex[SymmetricGroup[n], s]/.Table[s[i]->k+1, {i, 0, Binomial[n, 2]}], {n, 1, 7}], {k, 0, 6}]]//Grid (* Geoffrey Critzer, Jan 23 2012 *)
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CROSSREFS
| Columns give A000088, A004102, A053400, A053420, A053421.
Rows (4th and 5th) are listed in A063842, A063843.
Sequence in context: A122175 A073165 A137153 * A137596 A111669 A124834
Adjacent sequences: A063838 A063839 A063840 * A063842 A063843 A063844
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KEYWORD
| nonn,nice,tabl
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Aug 25 2001
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 03 2001
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